Question

the diagnols of a rectangle ABCD meet at O. If angle BOC=44, find angle OAD

Answer 1

$\Large{\underline{\underline{\bf{Given:-}}}}$

∠BOC = 44°

$\Large{\underline{\underline{\bf{To \:Find:-}}}}$

∠OAD = ?

$\Large{\underline{\underline{\bf{Solution:-}}}}$

we have,

⟹ ∠BOC + ∠BOA = 180° [linear pair]

⟹ 44° + ∠BOA = 180°

⟹ ∠BOA = 136°

Since diagnols of a rectangle are equal and they bisect each other. Therefore, in ∆OAB,

we have,

OA = OB

[ ∵ Angles opposite to equal sides are equal]

⟹ ∠1 = ∠2

Now, in ∆ OAB, we have

⟹ ∠1 + ∠2 + ∠BOA = 180°

⟹ 2∠1 + 136° = 180°

⟹ 2∠1 = 44°

⟹ ∠1 = 22°

Since each angle of a rectangle is a right angle.

∴ ∠BAD = 90°

⟹ ∠1 + ∠3 = 90°

⟹ 22° + ∠3 = 90°

⟹ ∠3 = 68°

Hence, ∠OAD = 68°

$\Large{\underline{\underline{\bf{Thanks}}}}$